x^2+x+1 .... compete square
(x^2+x+b^2)-b^2+1 ...........b=half of the coefficient of term x , so b=1/2
(x^2+x+(1/2)^2)-(1/2)^2+1
(x+1/2)^2-1/4+1
(x+1/2)^2-1/4+4/4
(x+1/2)^2 +3/4 -> square complete
you can also factor out 1/4 from (x+1/2)^2 to get 1/4 (2 x + 1)^2 + 3/4
